Friday, April 6, 2012
JCCDQBHWHCB019 Combinatorics : Circular Permutations
Suggested Approach and Solution:-
Draw a diagram. Let’s assume that the special woman (W*) is at the 12 o’clock reference position. [If not, we can always rotate our heads or rotate the table so that she is.]
Together with the two lucky(?) men M1 and M2, they form one entity. There are 3C2 x 2!
= 3P2 = 6 ways to choose and arrange these two men to sit besides this special woman. The other 4 persons can arrange themselves relative to the reference entity in 4! = 24 ways (this is same as (5 – 1)! or 5! / 5). Hence the number of ways = 6 x 24 = 144.